Riemannian symmetric spaces [chapter]

2010 Spaces of Constant Curvature  
How to cite: Jimenez, J. Alfredo (1982) Riemannian 4-symmetric spaces, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/7896/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata
more » ... de to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. ABSTRACT This thesis studies the theory of Riemannian "+-symmetric spaces. It follows the methods first introduced by E. Cartan to study ordinary symmetric spaces, and extended by J. Wolf and A. Gray and by Kac. The theory of generalized n-symmetric spaces was initiated by A. Ledger in 1967, and 2-and 3-symmetric spaces have already been classified. The theory of ^-symmetric spaces is completely new. The thesis naturally divides into two chapters. The first chapter treats the geometry of the spaces. Their homogeneous structure and their invariant connections are studied. The existence of a canonical invariant almost product structure is pointed out. A fibration over 2-symmetric spaces with 2-symmetric fibers is obtained. Root systems are used to obtain geometric invariants. Finally a local characterization in terms of curvature is obtained. Chapter II centers on the problems of classification. A local classification is given for the compact spaces in terms of simple Lie algebras. A global formulation is given for the compact classical simple Lie algebras. A final section is devoted to invariant almost complex structures. A characterization is given in terms of their homogeneous structure. It is shown that they can bear both Hodge and non-Kahler structures. DEDICATION A mi Esthercita hermosa y a mi jefazo, con todo mi carino y todo mi agradecimiento.
doi:10.1090/chel/372/08 fatcat:fbljmeoyizcmhhq7uynxtxhjne